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\title{Bayesian Estimation for Measuring Persuasion in Small Groups}
\author{Kevin M. Esterling (UC -- Riverside)}
\institute{}
\date{}


\begin{document}


\frame{\titlepage}

\section{Introduction}
\subsection{}

\frame[label=objectives]{
	\frametitle{Objectives of the video}
\begin{itemize}
\item What I hope to accomplish:
\begin{itemize}
\item Show how to implement the model in the paper \textbf{"When Deliberation Produces Persuasion Rather Than Polarization: Measuring and Modeling Small Group Dynamics in a Field Experiment"} by Kevin M. Esterling, Archon Fung and Taeku Lee (E.Funglee)
\item Show how to use \texttt{OpenBUGS} to replicate the results in the paper and/or to apply the general model to your own work.
\end{itemize}
\item What I don't intend to accomplish:
\begin{itemize}
\item Present the motivation or theory for the model or for the application to a deliberative field experiment
\item Teach you how to use \texttt{OpenBUGS} specifically, or Bayesian inference more generally
\end{itemize}
\end{itemize}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}

\frame[label=typesofmodel]{
	\frametitle{A general model for modeling dependence in small group research}
E.Funglee paper proposes a method to measure and evaluate persuasion in small groups.  
\begin{itemize}
\item This tutorial distributes code to preprocess your data and to implement the model
\item The models are flexible for the kind of outcome (continuous, dichotomous or ordered), the number of questions in your pre-post survey, and the number of respondents.
\end{itemize}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}




\section{Motivation}


\frame[label=motivation1]{
	\frametitle{}
\begin{figure}[htb]
	\begin{center}
		\includegraphics[scale=0.5]{oboe_discussion}
	%\caption{\label{fig:1}}
	\end{center}
\end{figure}
When people talk to each other in groups about some topic, we typically observe that preferences among group members become {\color{red} \textbf{dependent}}, through persuasion and other aspects of interpersonal interaction
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}


\subsection{}

\frame[label=motivation2]{
	\frametitle{Motivation for the model}
\textbf{Dependence in preferences typically occurs once people are in conversation with each other}
\begin{itemize}
\item This spatial dependence is induced by design in small group research
\item There are typically two sources of dependence:
\begin{itemize}
\item By homophily, similar people mutually select into groups
\item The group interaction itself can be causal, either by persuasion or by an affective process
\end{itemize}
\item The model in our paper accounts for and models both types of spatial dependence 
\item To use the model to measure the \textit{causal effect} of group interactions, all of the assumptions for an RCT must be met, and in particular randomization of participants to groups
\end{itemize}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}



\frame[label=twotypesdependence]{
	\frametitle{Two types of causal dependence}
Let's assume the RCT assumptions are met, as described in the paper, and so the model is measuring the causal impact of persuasion.  There are two types of persuasion
\begin{itemize}
\item Group composition effects: The effect of pretreatment characteristics of others in one's group, such as the distribution of ideal points or the demographic composition
\item Residual dependence within the group after accounting for any pretreatment covariates
\item \textbf{In order to model all of these forms of dependence, we need the model to keep track of who is nested in which group}
\end{itemize}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}


\frame[label=congdon]{
	\frametitle{}
\begin{figure}[htb]
	\begin{center}
		\includegraphics[scale=0.6]{congdon}
	%\caption{\label{fig:1}}
	\end{center}
\end{figure}
We derive the model from Congdon's book, chapter 8 -- please cite this book if you use this model!!
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}

\section{Data Setup}

\frame[label=datastructure]{
	\frametitle{What the data would look like if there was one group of four people?}
\begin{math}  
\hspace{110pt}\begin{array}{ccc} %block
 i & map & C \\ \hline
&& 0 \\ \hline
 1 & 2 & \\
& 3 & \\
 & 4 & 3\\ \hline
 2 & 1 & \\
& 3 & \\
 & 4 & 6\\ \hline
\ldots && \\
4 & 1 & \\
& 2 & \\
 & 3 & 12\\
 \end{array} %block 
\end{math} 
%\vspace{0.5in} \hspace{1.1in} \onslide<7>{\large{\textbf{\color<7>{green}Let's run this model in \texttt{OpenBUGS} \ldots}}}
}


\section{Application}
\subsection{}


\frame[label=motivationformodel]{
	\frametitle{The two types of causal dependence modeled in the E.Funglee paper}
\begin{itemize}
\item Group composition effects: In the paper, we test for the effect of the composition of ideal points within a group on the respondent's ideal point, which we label ``latent persuasion'' ($\Delta\theta$), which is identified because we nest respondents within questions
\item Residual dependence after accounting for any pretreatment covariates: In the paper, we test for the dependence of preferences within a group for a given topic after accounting for changes in a respondent's ideal point, which we label ``topic-specific persuasion'' ($\Delta\zeta$). 
\item Here I'll illustrate with an example for the continuous case \ldots
\end{itemize}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}



\subsection{}



\frame[label=implementation]{
	\frametitle{The E.Funglee model (for the simulated data)}
\begin{equation}
{\color<1>{red} O_{ik}^1 = \beta_{0k} + \beta_{1k}O_{i}^0 + \beta_{2k}\theta_i^0 + \beta_{3k}Site_i + {\color<2>{red} \Delta\theta_i} + {\color<3>{red} \Delta\zeta_{ik}} + \epsilon_{ik}} \label{e:model0}
\end{equation}
\begin{subequations}
\begin{align}
{\color<2>{red}\Delta\theta_{i}} & \sim  \phi(\Delta\theta_{i}^*, 1), \label{eq4a} \\
\Delta\theta_{i}^* & =  \alpha_{1}H_{i} +  (\delta_{1} \cdot Liberal_{i} + \delta_{3} \cdot Conservative_{i}) \cdot H^{2}_{i}  \\
H_{i} & =  \mbox{mean}(\theta_{ij}^0), \label{eq2b}  \\
\theta_{ij}^0 & \in  \left\{\theta_j^0 \mbox{ : \textit{j} is seated at \textit{i}'s table}, j \neq i \right\}. \label{eq2a} 
\end{align}
\end{subequations}
\begin{subequations}
\begin{align}
{\color<3>{red}\Delta\zeta_{ik}} & \sim  \phi(\Delta\zeta_{ik}^*, 1), \label{eq5b} \\
\Delta\zeta_{ik}^* & =  \rho_{k} \cdot \mbox{mean}(\Delta\zeta_{ijk}). \label{eq5c} \\
\Delta\zeta_{ijk} & \in  \left\{\Delta\zeta_{jk} \mbox{ : \textit{j} is seated at \textit{i}'s table}, j \neq i \right\}, \label{eq5a} 
\end{align}
\end{subequations}
\begin{center}
%\hyperlink{ideosd.densities}{\beamergotobutton{Empirical Distribution of Disagreement}}
\end{center}}




\end{document}



